Helmholtz-Institut für Strahlen- und Kernphysik

Time - Reversal  Invariance Test at COSY


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  Proposals   :  

The TRIC-experiment is planned as a novel high-precision test of time-reversal invariance, which conserves  parity. Using the internal circulating polarized proton beam of the COSY-ring at the Forschungszentrum Jülich and a tensor polarized atomic-beam target, the total cross-section asymmetry A y,xz is to be measured with an accuracy of 10-6. The general ideas of this measurement are described in the Proposal "Test of Time-Reversal Invariance in Proton-Deuteron Scattering" (Proposal I ). 
In view of the proposed test the measurement of the dominant error contributions is decisive for the accuracy of the TRIC experiment. In Proposal I it is argued that the total correlation coefficient Ay,y is the only observable in proton deuteron scattering, which can fake a TRI effect (see also TRIC for pedestrians ).
Since Ay,y is not known at 1 GeV which is the proposed energy for the TRI test Ay,y has to be determined. The measurement of this total correlation coefficient is explained in the Proposal "Measurement of the Total p-d Correlation Coefficient Ay,y by the TRIC Collaboration"  (Proposal II ).



Proposal I
Proposal II
Test of Time-Reversal Invariance in Proton-
Deuteron Scattering:
Measurement of the total p-d Correlation Coefficient
Ay,y by the TRIC Collaboration:
Motivation and General Description
Details of the Experiment
The Quantity of Interest
Beam Request
The Accuracy of the Experiment
Sources of Systematic Errors
Further Improvements and Conclusion



Test of Time-Reversal Invariance

  in Proton-Deuteron Scattering

Proposal by:

P.D. Eversheim, F. Hinterberger, J. Bisplinghoff, R. Jahn, J. Ernst

Institut für Strahlen- und Kernphysik der Universität Bonn, Germany

J. Dietrich, O. Felden, R, Gebel, M. Glende

Institut für Kernphysik, Forschungszentrum Jülich, Germany

H. E. Conzett

Lawrence Berkeley Laboratory, Berkeley, USA

M. Beyer

Institut für Theoretische Kernphysik der Universität Bonn, Germany

H. Paetz gen. Schieck

Institut für Kernphysik der Universität Köln, Germany

W. Kretschmer

Physikalisches Institut der Universität Erlangen, Germany


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We propose to perform a novel (P-even, T-odd) null test of time-reversal invariance to an accuracy of 10-4 (Phase 1) or 10-6 (Phase 2). The parity conserving time-reversal violating observable is the total cross-section asymmetry Ay,xz. The measurement is planned as an internal target transmission experiment at the cooler synchrotron COSY. Ay,xz is measured using a polarized beam with an energy above 1 GeV and a tensor polarized deuteron target.



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So far, the only link to a violation of time-reversal symmetry is given via the CPT-theorem and the observation of CP-violation in the neutral kaon system. Although the CP-violation could be accomodated by a complex phase of the Kobayashi- Maskawa-matrix1) or the theta-term2) allowed by QCD, other explanations go beyond the standard model, like for instance the extension of the Higgs sector3), the superweak interaction4), or the left-right symmetric models5). These extensions of the standard model may lead to interactions that are not related to the observed CP- or T-violation. Since the origin of the CP  or T-violation is not clear, further experimental tests of CP- or T-invariance outside the kaon system are necessary to probe the manifestation of the interaction responsible for the observed or possible new CP-violating effects.

In this context more direct information is expected from tests involving elementary particles compared to tests involving complex nuclei. In addition, we intend to probe the time-reversal invariance with parity being conserved in contrast to experiments which test parity and time reversal invariance (TRI) simultaneously (cf. tests of the electric-dipole moment of elementary particles).

Usually P-even TRI tests compare two observables (cf. tests of detailed balance or P A tests). Since in these experiments two observables have to be compared, the experimental accuracy6) was limited to 10-3 - 10-2. The accuracy can be increased by orders of magnitude if a true null experiment is performed i.e. a non-vanishing value of one single observable proves that the symmetry involved is violated. An example of this kind of experiment is the measurement of the parity violating quantity Az in proton-proton scattering7), which has been measured to some 10-8 (cf. Table 1). In this context the term “true” stresses the concept that the intended test has to be completely independent from dynamical assumtions. Therefore, the interpretation of the result is neither restricted nor subject to: Final state interactions, special tensorial interactions or, Hamiltonians of a certain form. True null tests are based only on the structure of the scattering matrix as determined by general conservation laws8).

It has been proven8) that there exists no true null test of TRI in a nuclear reaction with two particles in and two particles out, except for forward scattering. Based on this exception, Conzett9) could show that a transmission experiment can be devised, which constitutes a true TRI null test. He suggested to measure the total cross-section asymmetry Ay,xz of vector polarized spin 1/2 particles interacting with tensor polarized spin 1 particles.

We intend to study this observable Ay,xz in the proton-deuteron system with the proton polarization Py along the y direction and the deuteron tensor polarization Pxz a­ligned along the x=z direction. The proton-deuteron system has the advantage of being a particularly simple system allowing still a direct analysis in terms of time-reversal violating (TRV) nucleon-nucleon potentials based e.g. on one meson exchange. In addition, the proton-deuteron system offers the opportunity to test simultaneously the p-p and the p-n interaction. According to a theorem of Simonius10), the n-p system is favoured over the p-p system as a TRI testing ground in view of the symmetry restrictions on possible TRV meson exchange processes. In principle, both systems can be tested with the intended experiment.


Table 1

Comparison of accuracies of TRI and Parity-violation tests

    Measurement     Remarks
    Electric dipole moment of the neutron     gPT   <=   10-11
    gamma-gamma correlation in  57Fe     aT   <=   5·10-6
    P-A in p-p scattering     gT   <=   3·10-2
    Detailed balance in p + 27Al  <->  4He + 24Mg     aT   ~ gT <=   10-3
    n-transmission through 139 La     Hope for enhancement
    n-rotation in 139La     Enhancement ~ 105
    Az     in p-p scattering     Error(Az) ~ 2·10-8
    Ay,xz    in p-d scattering     This experiment

  g :   strength of Todd NN potential
  a :   strength of an effective Todd N-core potential

The TRI test can be performed at any beam energy. But since the TRV processes are of short-range nature - the long range contributions for these processes may be param­eterized by vector meson or f1 axial-vector meson exchange17) - the experiment is intended to be performed at about 1 GeV.

We intend to study the TRV quantity Ay,xz in a transmission experiment using an internal deuteron target in the cooler synchrotron COSY. The tensor polarized deuteron target is prepared using the polarized atomic beam target facility of the COSY experiment #5 (phase 1). Phase 2 is characterized by an improved control of systematic error contributions and the addition of a target cell to the polarized atomic beam target. The transmission losses of the circulating polarized proton beam are measured with high precision as a function of the vector- and tensor-polarization Py and Pxz, respectively. Thus, for this experiment the COSY facility is not only used as an accelerator, but also as an ideal forward spectrometer and detector.


The Quantity of Interest

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A transmission experiment involving polarized particles is described by the general­ized optical theorem18) :

  T    =    4 Pi / k   Im(Tr rho · F(0))                                                                                                            (1)
T – Total cross section
k – Wave number
rho – Density matrix
F(theta) – Scattering amplitude matrix for scattering at angle theta

The density matrix reflects the experimental set-up, whereas the scattering matrix F(0) of the forward scattering amplitudes contains the physics, which is to be tested. In the following it is shown which observable conserves parity but violates time-reversal and that the time reversed situation is tested by flipping the spin.


The discussion of parity conserving (P-even) TRV (T-odd) observable follows the arguments of Ohlsen19). It is discussed in the projectile helicity frame i.e.:

ez = ekin                          with: e is a unit vector pointing in the direction of x, y, z, kin and kout                       (2)
ey = ekin x ekout
ex = ey x ez

Since for a transmission experiment ekout is parallel to ekin, the direction of ey can be chosen at will. A convenient choice is to have ey parallel to the proton polarization Py.


In general a polarization observable describing a process of two particles having tensor polarizations of ranks r and r´ is characterized by a quantity with a number nr of indices with: nr = rin + r´in + rout + r´out. Each index specifies whether the polarization is observed in x, y, z-direction or not at all (index=0).

For the intended transmission experiment only the initial states are of interest, thus: nr = rin + r´in. Furthermore, the quantity of interest has to be invariant under the rotation about the z-axis (Rz-even). Rz invariance means to have an observable that behaves odd or even as a function of the scattering angle theta. Equivalent to this condition behaves the sum of the indices nx+ny, which is odd or even, respectively. All "odd" quantities with this respect rule out to the degree that the acceptance angle of the detector (i.e. COSY) is small. Since COSY can be tuned to have a small acceptance angle without a significant loss in luminosity, a decisive advantage over an external (spectrometer) experiment is given.

According to Ohlsen19), the symmetry character of a polarization amplitude with nr = nx+ny+nz indices can be determined by "counting rules". nx , ny , and nz are the numbers of x, y, and z indices of the observable in question. In detail the following counting rules apply for a P-even, T-odd, and Rz-even quantity:

  Time-reversal :                nx has to be odd

Parity conservation :      nx+ nz has to be even                                                         (3)

Rz invariance :                nx+ ny has to be even


The minimal configuration fulfilling these conditions gives:

  nx = ny = nz = 1                                                                                                      (4)



  Fig. 1 Beam and target spin-alignment in the laboratory projectile helicity frame

  Assuming a proton beam with normal polarization Py, the target has to be at least a spin 1 particle, in order to be able to offer a tensor polarization Pxz aligned in the x=z direction. Deuterons fulfill this requirement. Thus, the quantity of interest is the total cross-section asymmetry Ay,xz for proton-deuteron scattering (cf. Fig. 1). Ay,xz is meas­ured by flipping the spins of the interacting particles. By flipping the spins in this particular system the time reversed situation is prepared too. This is shown in Fig. 2a-c by reversing all momenta and spins and exchanging the in- and out-going particles.

  Ay,xz is measured in a transmission experiment. This process is described by the transmission factor T(N):

T(N)    =    I(N) / I(0) =    exp (-T · rho · d · N )                                                                                        (5)
I(0) – Intensity of the primary beam
– Intensity of the beam having passed N times the
   internal target with the thickness d and density rho
T – Total cross section


For the case of polarized particles T has to be replaced by:

T    =    y,xz + Loss    =    o (1 + Py Pxz Ay,xz ) + Loss                                                                 (6)
o – Unpolarized total cross-section
– Loss cross-section, taking account of beam losses
   outside of the target
Py – Proton y-Polarization
Pxz – Deuteron xz-Polarization
Ay,xz – Total cross-section asymmetry


In order to measure Ay,xz the transmission asymmetry Ty,xz is introduced:

Ty,xz     =     (e -x+  -  e -x- )   /   (e -x+  +  e -x- )     =     ( T+  -  T- )   /   ( T+  +  T- )                            (7)
– Transmission factor for the proton-deutron spin-configuration
   Py > 0, Pxz > 0
– Transmission factor for the time reversed situation
   i.e. either   Py < 0   ,   Pxz < 0
X+ / -
– Chi is the Product of the factors ( T · rho · d · N )
   with respect to the proton-deuteron spin-alignment


this gives:

Ty,xz     =     - tanh (o · rho · d · N    Py   Pxz   Ay,xz )                                                                          (8)

Is the argument of the tanh in equation (8) small, then:

Ty,xz     =     - o · rho · d · N    Py   Pxz   Ay,xz                                                                                     (9)

With the help of equation (9) the total cross-section asymmetry Ay,xz can be determined.



  Fig. 2 Pictorial demonstration that a time-reversed situation is prepared by either a proton or a deuteron spin-flip. a) The basic system is shown. b) The time reversal operation is applied (momenta and spins are reversed and the particles are exchanged). In order to have a direct comparison between situation a) and b), two rotations Ry (Pi) or Rx(Pi) by 180o about the y- or x- axis are applied, leading to the situations c) and d), respectively. This is allowed, since the scattering process is invariant under rotations.

– Proton spin up (y-direction)
– Proton spin down
– Deuteron tensor polarization


The Accuracy of the Experiment

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Basically, the experimental set-up only needs equipment that is provided for other experiments, i.e. a polarized proton beam in COSY, an atomic beam source producing polarized protons and deuterons for internal target experiments, and an on-line current monitor20) of high precision that is a standard diagnosis device for the operation of COSY.

A typical measurement sequence may be:

i)   The polarized proton beam is injected into the COSY ring and is accelerated to the appropriate energy  
ii)   The atomic beam source is switched on, to give pure deuteron tensor polarization Pxz
The loss rate is eliminated by flipping the deuteron tensor polarization and eventually the proton vector polarization Py randomly
The beam is decelerated and dumped. Until the next sequence starts, the polarimeter in the deuteron beam-dump is calibrated  


In   the following, an upper limit of the accuracy that can be achieved is estimated from the shot noise of the scattered particles. For a two weeks run the beam is assumed to be on target for 10 days. With an unpolarized cross-section o = 80 mb the following accuracies for various beam intensities and target thicknesses are calculated (Table 2):


Table 2

Accuracy of this experiment calculated from basic statistics for
  phase 1 (rho· d = 1012 atoms/cm2) and phase 2 (rho·d = 4·1014 atoms/cm2)

    Protons in COSY ring     Target thickness
Basic statistics
    1.3·109     1012   atoms/cm2
    1.3·1011     1012   atoms/cm2
    1.3·1011     4·1014   atoms/cm2


For a conservative estimation of the accuracy that can be achieved, the sensitivity S is introduced in equation (9):

Ty,xz     =     - S · Ay,xz                                                                                                                      (10)

Equation (10) defines S:

S     =     o · rho · d · N    Py   Pxz                                                                                                        (11)

With a spin-flip every 5 s and with:

rho · d =   4 · 1012   atoms / cm2
o =   80 mb                                                                                                                                  (12)
N =   1.5 · 106   turns / s   · 5s    =    7.5 · 106   turns
Py Pxz =   1


S becomes:    S = 2.4 · 10-4.


The precision of the transmission asymmetry Ty,xz is calculated from the precision of the current measurement. For 1.3 · 1011 protons in the COSY ring the current is measured within 40  ms to a precision of 5 · 10-5. Within 10  days the precision of the transmission asymmetry Ty,xz is measured to 1 ·10-8. With equation (10) the accuracy delta Ay,xz of the total-cross-section asymmetry Ay,xz is calculated: delta  Ay,xz = 4 ·10-5.

The accuracy of Ay,xz can be further improved by increasing the sensitivity S or by improving the precision of the Ty,xz measurement. The sensitivity can be improved  by extending the spin-flip period, for instance from 5s to 50s. As a consequence the number of turns N and hence the sensitivity S is increased by an order of magnitude. In case the precision of the current measurement is improved simultaneously by an order of magnitude the precision of Ty,xz is improved accordingly, and delta Ay,xz reduces to 4·10-7. Un­der these conditions delta Ay,xz is dominated by the shot noise of the underlying statistics of the scattering process, and it becomes increasingly important to discuss in more detail the handling of systematic errors.


Sources of Systematic Errors

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Two obvious experimental effects are discussed: i) the loss of the beam intensity somewhere in the ring except in the target zone, and ii) competing polarization observables.

i)   The effect of beam losses in the ring cancels in equation (7), since it is not related to the proton- or deuteron-polarization  
ii)   All polarization observables in proton-deuteron scattering for this type of experiment are listed in Table 3  


If Ay,xz is calculated from changing the proton polarization each time the ring is filled, all observables of Table 3 in line 1 and 5 cancel. Since only the proton polarization Py is an eigenvector in the ring, all observables with respect to the proton polarization Px and Pz cancel too (the average of Px and Pz should be < 10-8 in a 10 days run). This is true for lines 2, 4, 6, and 8 in Table 3.

In the remaining lines 3 and 7 of Table 3 all quantities with a hat cancel, because they are not Rz-even (nx+ny has to be even). Ay,x and Ay,yz violate parity conservation (nx+nz is odd for these quantities). Therefore, since p - d scattering is an elementary process, these quantities are expected to be of the order of 10-7, even if parity is violated. Thus, besides our quantity of interest Ay,xz, only Ay,y "survives ".


Table 3

Polarization observables of the total cross-section in p-d scattering.
  The first index refers to the proton polarization, the second and third index refers to the
  deuteron vector- and tensor polarisation.

    Line     Observable     Line cancels because of:
    1      Io,o         Âo,x        Âo,y        Ao,z     proton-spinflip
    2      Âx,o        Ax,x        Ax,y        Âx,z     Px negligible for protons
    3      Ây,o        Ay,x        Ay,y        Ây,z     
    4      Az,o        Âz,x        Âz,y        Az,z     Pz negligible for protons
    5      Ao,xx        Ao,yy        Ao,zz        Ao,xy        Âo,yz        Âo,xz            proton-spinflip
    6      Âx,xx        Âx,yy        Âx,zz        Âx,xy        Ax,yz        Ax,xz            Px negligible for protons
    7      Ây,xx        Ây,yy        Ây,zz        Ây,xy        Ay,yz        Ay,xz            
    8      Az,xx        Az,yy        Az,zz        Az,xy        Âz,yz        Âz,xz            Pz negligible for protons

All quantities with a hat cancel, since they are Rz-odd (nx+ny has to be even).


The latter quantity is small, because i) there must be a deuteron vector polarization in the first place, and ii) there must be a misalignment between the COSY beam direction and the deuteron beam, so that a deuteron vector polarization is able to generate a Py deuteron vector polarization. The deuteron vector polarization can be adjusted to be zero in the atomic beam source, if this polarization is measured in the dump of the atomic beam source. The quality by which this is done makes the difference between phase 1 and phase 2 of this experiment.

Without major effort (phase 1), the deuteron polarization Pz can be limited to a few percent. The deuteron source and the proton beam can be aligned to better than 0.1o, resulting in a false deuteron polarization Py < 10-4, which limits the accuracy attainable in phase 1 of the experiment.

The deuteron vector- and tensor-polarization can for instance be measured in a scattering experiment via the d+d reaction21) at 30 keV or rather by measuring the change of the atomic beam intensity with the aid of a quadrupole-mass-spectrometer. In this case the deuteron beam dump has to be replaced by an arrangement of two 6-pole magnets and at least two RF-transitions (principle of an "inverted" nuclear spinpreparation system of a ground-state atomic beam source). Alternatively, a spin-filter can be used, which is essentially the spin-preparation module of a Lamb-shift source. The installation of either of these three methods provides a precise determination of the deuteron vector- and tensor-polarization and is mandatory for phase 2 of the proposed experiment.


Further Improvements and Conclusion

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The precision of the standard COSY current monitors can be improved for our purpose by an order of magnitude22), which would improve the precision of the transmission asymmetry Ty,xz measurement accordingly. The precision of the standard COSY current monitors is limited by the Barkhausen noise of its ferrits. Using the fast pick-up devices of the stochastic cooler tanks of COSY with its cooled FET-amplifiers provides lower noise current monitors. Moreover, because there are several such devices placed about the COSY ring, the precision of the current measurement can be improved further.

Even without these improvement the quantity of interest Ay,xz can be measured in phase 1 and phase 2 to an accuracy of 10-4 and some 10-6, respectively. The accuracy of this novel P-even, T-odd true null test of time-reversal invariance is neither limited by the available statistics nor the precision that can be achieved, rather than by systematic error contributions . Below an accuracy of 10-6 special attention has to be payed to systematic error contributions of observables that are sensitive to parity violation.



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1)     M. Kobayashi, T. Maskawa, Progr. Theor. Phys. 49 (1973) 652

2)     R.J. Crewther et al., Phys. Lett. 88B (1979) 123

3)     S.L. Glashow, Nucl. Phys. 22 (1961) 579

4)     L. Wolfenstein, Ann. Rev. Nucl. Part. Sci. 36 (1986) 137

5)     J.C. Pati, A. Salam, Phys. Rev. D10 (1974) 275

6)     H.L. Harney et al., Nucl. Phys. A518 (1990) 35

7)     COSY Proposal #3, P.D. Eversheim et al., Phys. Lett. B256 (1991) 11, S. Kistryn et al., Phys. Rev. Lett. 58 (1987) 1616

8)     F. Arash, M.J. Moravcsik and G.R. Goldstein, Phys. Rev. Lett. 54 (1985) 2649

9)     H.E. Conzett, 7th Intl. Conf. on "Pol. Phen. Nucl. Phys.", Paris (1990) 2D

10)     M. Simonius, Phys. Lett. B58 (1975) 147

11)     N.F. Ramsey, Ann. Rev. Nucl. Sci. 32 (1982) 211

12)     M. Beyer, Nucl. Phys. A493 (1989) 335 and N.K. Cheung, H.E. Henrikson, F. Boehm, Phys. Rev. C16 (1977) 2381

13)     C.F. Hwang et al., Phys. Rev. 119 (1960) 352

14)     E.Blake et al., Phys. Rev. Lett. 51 (1983) 355

15)     V.E. Bunakov, Phys. Rev. Lett. 60 (1988) 2250

16)     Y. Yamaguchi, J. Phys. Soc. Jpn. 57 (1988) 1518

17)     M. Beyer, Nucl. Phys. A560 (1993) 895

18)     C. Bourrely, E. Leader, J. Soffer, Phys. Rep. 59 (1980) 95; note that their equation (3.41) is not the most general one, since rho is in general not a real matrix

19)     G.G. Ohlsen, Rep. Progr. Phys. 35 (1972) 717

20)     K.B. Unser, CERN/SL/90 27 (BI)

21)     B. Polke et al., 7th Intl. Conf. on "Pol. Phen. Nucl. Phys.", Paris (1990) 57B, and H. Paetz gen. Schieck, private communications.

22)     Private communications, S. Vigdor IUCF Bloomington, USA and P. von Rossen COSY Jülich, Germany



Proposal for

Measurement of the Total Correlation Coefficient Ay,y
  by the TRIC Collaboration

D. Eversheim for the TRIC collaboration


1)   Motivation and General Description

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In view of the proposed Test of Time-Reversal Invariance (TRI) in Proton-Deuteron Scattering [1-8] at COSY (proposal #22) the measurement of the dominant error contributions is decisive for the accuracy of the TRI experiment. In the TRI proposal it is argued that the total correlation coefficient Ay,y is the only observable in proton-deuteron scattering, which can fake a TRI effect.

Since the total correlation coefficient Ay,y is not known at 1 GeV which is the proposed energy for the TRI test Ay,y has to be determined. The experiment is to take place at TP2 and thus the EDDA detector can be used as an internal polarimeter. Ay,y shall be measured in two ways:

i) The circulating polarized proton beam at 1 GeV interacts with the polarized deuteron beam from the atomic-beam target for EDDA [6,9]. Asymmetries with respect to the spin configuration of the beam and the target are measured over the total angular acceptance of the EDDA detector.

ii) The measurement is performed by observing the decrease of the circulating current in COSY as a function of the spin alignments of the beam and the target (this method is described in detail in the TRI proposal #22 [1])

Method i) is very useful for studying systematic errors of the measuring principle. Since the angular acceptance of the EDDA detector does not cover completely 180o and the elastic channel is preferentially analysed, Ay,y is only approximately determined.

In contrast, method ii) measures all inelastic channels and regards the complete angular range from 0o-180o, since the forward scattering amplitude is measured via the transmission asymmetry Ty,y. Ty,y contains Ay,y, the quantity of interest for this experiment in the same way as Ty,xz contains Ay,xz, the quantity of interest for the TRI test (cf. the TRI proposal ). Thus a novel type of internal experiment will be established that utilizes the COSY ring not only as an accelerator but also as an ideal forward spectrometer and detector.

2)   Details of the Experiment

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The apparatus for method i) is the usual EDDA set-up with a special RF-transition for the polarized atomic-beam target, which provides a vector polarized deuteron beam (Pz = 1) This transition has been developed in the diploma thesis of Dirk Lorenser, University Bonn. Since only weak holding fields across the interaction zone are allowed at COSY, a pure deuteron state has to be prepared. This in turn implies that simultaneously the atomic deuteron beam will be tensor polarized (Pzz = 1). On the other hand, switching off the RF-transitions provides a deuteron beam with Pz = 1/3 and Pzz = –1/3 at the exit of the target. The holding field is vertically aligned so that the vector- and tensor-alignment is adiabatically changed to Py and Pyy at the interaction zone.

Since the holding field is provided by ferrite cored electric magnets, a fast spin-flip (< 1ms) can be provided. Switching off the RF-transition gives a different linear combination of deuteron vector- and tensor-polarization. Finally, interspersing sequences with an unpolarized proton beam, allows to extract Ay,y. In more detail, according to Ohlsen [10], for a vertical holding field, the following quantities are of interest:




, – polarized, unpolarized differential cross-section
py, pyT, pyyT – beam, target vector- and tensor-polarization
Ay, AyT, AyyT – beam, target vector- and tensor-analyzing power
Ayy,y – target-beam tensor-vector correlation
Ay,y – target-beam vector correlation
– all underlined quantities are odd functions of the azimuth-angle


If the Left-Right asymmetries are not measured with the EDDA detector, all underlined quantities do not contribute. Providing an unpolarized proton beam with the flipping of the holding field and the RF-transition switched on- and off, allows to determine Ayy and . Then, with a polarized proton beam, Ay,y the quantity of interest can be determined as soon as the proton spin is flipped.

Since for method i) it has been shown that by proper combinations of spin flip and switching on- and off the RF-transition the total amount of scattered particles is changed, the transmission is changed accordingly. Therefore, Ay,y can be deduced from a transmission asymmetry too.

3)   Beam Request

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Given a cross-section of 80 mb, a target density of 2·1011 deuterons/cm2, an intensity of 1010 polarized protons circulating at 1 MHz, results in a total rate of 160 Hz. Under these conditions for the scattering experiments some hours should be sufficient for a precision of some percent.

The TRIC collaboration is asking for 6 days of beam-time splitted in 2 periods of 3 days each. These periods should preferably be scheduled following a beam development week. The time is intended for the following purposes:

  1)    Establish a method to determine an estimate for the total correlation coefficient Ay,y.

        Especially:     a)   Study the quality of the deuteron polarization.

              b)   Study the quality of the polarized proton beam

              c)   Study systematic error sources

2)    Establish a novel measuring technique for a ring-accelerator. Use the EDDA detector as an efficient polarimeter and luminosity monitor.


4)   References

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1)  COSY Proposal #22: “Test of Time-Reversal Invariance in Proton-Deuteron Scattering”

2)  P.D. Eversheim

Proc. of the 2nd Adriatico Research Conf. on Pol. Dynamics in Nuclear and Particle Phys., Triest, Italy, World Scientific (1992) 142

3)  P.D. Eversheim, F. Hinterberger, J. Bisplinghoff, R. Jahn, J. Ernst, W. Kretschmer, H. Paetz gen. Schieck, and H.E. Conzett

AIP Conference Proceedings 339 (1994) 191

4)  P.D. Eversheim

     Int. Workshop on Pol. Beams and Pol. Gas Targets, Cologne, Germany

     World Scientific (1996) 224

5)  P.D. Eversheim, F. Hinterberger, J. Bisplinghoff, R. Jahn, J. Ernst, M. Beyer, H. Paetz gen. Schieck, W. Kretschmer and H.E. Conzett

     12th Int. Symp. on High-Energy Physics, Amsterdam, The Netherlands

     World Scientific (1996) 303

6)  P.D. Eversheim, M. Altmeier, and O. Felden

      Nucl. Phys. A626 (1997) 117c

7) P.D. Eversheim, F. Hinterberger, J. Bisplinghoff, R. Jahn, J. Ernst, H. Paetz gen. Schieck, W. Kretschmer, and H.E. Conzett

AIP Conference Proceedings 421 (1997) 501

8)  P.D. Eversheim

     Nucl. Phys. A629 (1998) 471c

9)  P.D. Eversheim, M. Altmeier, O.Felden, M. Glende, M. Walker, A. Hiemer, and R. Gebel

AIP Conference Proceedings 421 (1997) 419

10)  G.G. Ohlsen

      Rep.Prog.Phys. 35 (1972) 760